8/19/04 SYLLABUS ‑ MATH 3195: Elementary Differential Equations and Linear Algebra

Fall Semester ‑ 2004
 

Professor: Weldon A. Lodwick

Office: CU-Denver Building, Room 622

Telephone: 556‑8462 (office - voice mail), 556‑8442 (secretary), 556-8550 (fax)

Note: If you fax your work, make sure my name appears on the first page, your work has a page number on each page and that your name is on each page.

E-Mail: wlodwick@math.cudenver.edu

Web Site: http://www-math.cudenver.edu/~wlodwick

Text:       Differential Equations & Linear Algebra by J. Farlow, J. Hall, J. McDill, and B. West, Prentice Hall, 2002.

 

Office Hours:       Mondays                               4:30-5:30pm           622 CU-Denver Bldg

                                Tuesdays/Thursdays          9:45-10:45am          130 Science – MERC Lab

                                Tuesdays                              3:45 - 4:45pm         622 CU-Denver Bldg

Other times by arrangement

 

Students with Disabilities: If you have a disability that requires accommodation in this course, please see me as soon as possible.  I am happy to make appropriate accommodations, provided timely notice is received.

 

Cell Phones: Please turn off your cell phones prior to entering the classroom.  This is especially important when coming in for exams.

 

MY APPROACH TO TEACHING

I believe that teaching is a process that involves an active partnership.  My role is that of a guide to your learning.  We will endeavor to discover how we mathematically know within the structure of this course.  If we have a mathematical problem, it is because we don’t know its solution.  If we knew the solution, we would not have a problem.  Thus, when we “solve” the problem, how do we know the answer we obtain is the solution to our problem?  Thus to know mathematically (mathematical epistemology) is a central component of my teaching approach.  This means that I believe it is important to know how one obtains the solution to a mathematical problem.  Thus, it is imperative that you demonstrate the process by which you arrive at a solution, that is, you are to demonstrate knowledge of mathematics by articulating how you obtained the correct solution.

 

I believe that I am responsible to open the way, to encourage, and to, perhaps, nudge you toward your own learning.  I will help guide you toward this learning by providing mathematics for you to experience.  It is my aim to communicate mathematics in a way that is supportive of your efforts. Your role is to find a way to experience and articulate the mathematics that is presented and that you encounter.  I believe that it is your responsibility to let me know when you find yourself not understanding mathematical concepts that are presented in class.  Once you make this known, it is our responsibility to work on trying to attain clarity.  I will try to be as proactive as possible.  I believe that results on examinations, quizzes and projects give us the opportunity to clearly see where the areas of mathematical understanding are and what areas need more attention.

 

EVALUATIVE CRITERIA

There are three evaluative criteria: in-class exams, in-class quizzes and projects.  On quizzes and exams and assignments, you are always to show your work sufficient for me to understand how you obtained your answer.

 

EXAMS: There are three exams (1.5 hours each) and a comprehensive final (2 hours).  The final exam covers all the material we’ve studied in the semester roughly equally weighted.  All exams are in-class, closed book, closed notes (no “cheat” sheet) and open mind.

 

Note about asking me questions during an exam.  I will NOT answer questions about the exam.  Understanding what the problem is asking is part of the problem.  It may be the case that for a problem, there will be someone for whom the problem is not clear.  Everyone must work with the problems as stated.  If you think the problem is in error, please correct the error and state precisely what was in error and how you corrected it.  Then continue with the problem.  If you are correct, you will receive full credit and perhaps a bonus if the correction is more than a typo.  If you were to come up and ask for help on a problem, you disturb others.  A colleague and I will take the exam prior to your taking the exam.  Thus, the exam will have been “debugged” and tested to the best of our ability.

 

QUIZZES: There will be 10 in-class quizzes given noon – 12:10pm on the following Tuesdays:

August 31, September 7 and 14, October 5, 12 and 19, November 2, 9 and 16, December 7.  Each quiz will have two problems of which you choose one to answer and each quiz is worth 12.5 points so you will have extra credit in case you miss a quiz.  That is, I do not give make-up quizzes.  The extra 2.5 points per quiz is the make-up.  The maximum number of points possible is 100 so that you do not have to ask about being excused unless you miss more than two quizzes for legitimate reasons.    The problems will be taken from the “minimal set” listed below.  Thus, I will not collect problems to grade.  You can practice on the “minimal set” and ask me questions about these during office hours. 

 

PROJECTS: The instructions and descriptions will come later.

 

GRADE POINT DISTRIBUTION

Evaluative Criterion

POINTS POSSIBLE

POINTS

Projects

2x100

200

Quizzes

10x10

100

Exams

3x100

300

Final

200

200

Total

 

800

 

I do give +/- unless your school does not recognize +/- grades in which case I grade without +/-.

 

A   = 94%-100%   B+ = 88%-90%  C+ = 78% - 80%  D+ = 68% - 70%

A   = 94%-100%   B   = 84%-87%  C   = 74% - 77%  D   = 64% - 67%

A- = 91%-93%      B- = 81%-83%  C-  = 71% - 73%  D-  = 60% - 63%

F  less than 60%

 

Note, if your school (for example the School of Engineering) does not. recognize +/-, then an A is 93% to 100%, B is 82.5% to 92.9%, C is 72.5% to 82.4%, D is 60% to 72.4% and an F is less than 60%.

 

General advice: Keep all materials that I turn back in case you think I have not credited you with the points you earned.  I can only correct your score if you have what I have turned back to you. It is a good idea to xerox anything that you turn in just in case I lose what you turn in.  Please check to make sure that the points you earned are the points I have recorded.  The statistics that I have read about correctness of professors in grading and recording grades state that there is a 6% error rate.  Please make sure that I have correctly graded and recorded your points.

 

Advice on exam taking: Some exams may be longer (or more demanding or both) than what you are accustomed.  Thus, it is wise (imperative) for you take exams as follows.  Do all the problems you can do first.  Don't waste too much time on making sure that you have done your arithmetic correctly since arithmetic mistakes are usually discounted at half a point per mistake unless your arithmetic mistake totally trivializes the problem in which case the deduction will be severe.  That is, you should work on generating the most number of points per unit of time – the maximum number of points per minute.

 

POLICIES

Drops and incomplete grades: See Schedule of Courses for the relevant dates with respect to dropping this course.  The incomplete policy of the Mathematics Department and the College of Liberal Arts and Sciences is strictly enforced.  Incomplete grades are given only in situations in which a student who has been in good standing all semester, is prevented from completing a course assignment (for example the final exam) due to circumstances beyond her/his control (for example, hospitalization, jury duty, revised job assignments, death in the family).

 

Missing Examinations: If you miss a test for acceptable reasons and we have met before the test and agreed that indeed this is the case you will be given a make-up exam.  You are to take the final exam on the given date.  If you have more than two final exams on date of our final, this will have to be resolved at least one week in advance of our final exam.  There are cases where an exam is missed without your being able to notify me ahead of time.  These will be exceptional cases and we can work these out as long as your reasons are legitimate.

 

Legitimate Excuses: Legitimate excuses for missing tests and quizzes are for some situations that are beyond your control.  You may be required to produce official, signed documentation.  If you are needed in a wedding, for example, you must talk to me prior to the (blessed) event.  If you are legally arrested, then this is not a legitimate excuse.  For matters that are within your control, the general rule is that it is not excused.  However, talk to me prior to the event.

 

University Dates to Keep in Mind

16 August: (5:00 pm) Payment plan deadline for students registering by 23 July 2004

18 August: Students not on financial aid are dis-enrolled for non-payment. 

26 August:  Last day to select the wait-list for a closed course.  Students should check wait-list status

daily.

30 August - 8 September: Students are responsible for verifying an accurate Fall 2004 registration

via SMART.

2 September (midnight):  Last day to add courses via the web SMART system.

6 September:  Labor Day, no classes.

8 September (5:00 pm) Last day to add 16-week structured courses.  Treated as an absolute deadline.

The 8 Sept. add deadline does not apply to independent study, internships, and late-starting courses.

8 September (5:00 pm): Last day to drop a course for full refund.  Last day to select P/F grade option

1 November: Last day to drop a Fall 2004 course without associate dean approval.

12 November: Last day to drop a Fall 2004 course for CLAS students.  Treated as an absolute

deadline.

21-27 November: Full week of Fall Break, no classes.

11-17 December: Final Exam week.


 

Tentative Syllabus and Problem Assignments

Day

Topics

Reading

Problems (Minimal Set)

Aug 24

Dynamical systems, mathematical models

Prologue, 1.1

22, 24

Aug 26

Solutions, direction fields

1.2

3, 5, 7, 9, 13-18, 23, 35

Aug 31

Separable ODEs, Euler’s method

1.3, 1.4

5, 9, 13, 15, 19-24, 53

Sept 2

Properties of linear ODEs

2.1

3, 7, 11, 19, 37

Sept 7

Solutions of first order linear ODEs, integrating factors

2.2

3, 7, 13, 17, 19, 27, 29, 31, 34

Sept 9

Exponential growth and decay models

2.3

7, 11, 15, 21, 25, 29

Sept 14

First order ODE models: mixing, cooling, harvesting, loans annuities

2.4

3, 7, 8-9, 15, 17, 19

Sept 16

Nonlinear models

2.5

3, 13, 17, 27

Sept 21

EXAM 1 – Chapters 1 and 2

Sept 23

Matrices, vectors, geometry

3.1

Review 1-30, 45, 57, 59, 61

Sept 28

Systems of linear equations

3.2

3, 5-9, 13, 17, 21, 27, 29, 31, 41

Sept 30

Inverses and determinants

3.3, 3.4

5, 7, 14, 18; 1, 12, 13, 23, 33

Oct 5

Vector spaces

3.5

3, 10, 11-19, 25, 37-46, 62

Oct 7

Basis and dimension

3.6

3, 5, 9, 11, 15, 19, 23, 27, 37, 39, 43, 45, 47,

Oct 12

2nd order ODEs, phase plane, circuits and oscillators.

4.1

5, 12, 13, 15, 17, 23, 25, 29, 31, 34, 37, 47,

Oct 14

2nd order ODEs; real roots

4.2

7, 11, 15, 19, 21-24, 25, 35, 37, 47

Oct 19

2nd order ODEs; complex roots

4.3

5, 9, 13, 19, 21, 41, 43

Oct 21

EXAM 2 - Chapter 3, 4.1 and 4.2, MINI-PROJECT #1 DUE

Oct 26

Non-homogeneous problems and forced oscillations

4.4, 4.5

5, 13, 15, 17, 23, 29; 1, 7, 8-11, 12, 13, 17

Oct 28

Linear transformations

5.1, 5.2

1-13, 17, 24-26, 33, 37, 39, 43, 52, 79; 3, 5, 9, 13, 23, 29, 35, 45, 49,

Nov 2

Eigenvalues

5.3

3, 5, 9, 21, 22, 39, 43, 47, 50

Nov 4

Systems of linear ODEs

6.1

3, 7, 9, 15, 23-26

Nov 9

Systems with real eigenvalues

6.2

3, 9, 13, 19, 23, 43

Nov 11

Systems with complex eigenvalues

6.3

3, 7, 13, 15, 19,

Nov 16

Stability and chaos

6.5

1, 3, 5

Nov 18

EXAM 3 – 4.3-4.5, Chapter 5, 6.1-6.3

Nov 21-27

FALL BREAK

Nov 30

Laplace transforms

8.3

3, 7, 9, 13, 17, 27, 29, 33, 35, 41, 45, 49, 53, 57, 58, 61, 63

Dec 2

Laplace transforms

8.4

3, 11, 17, 27, 31, 35, 37, 59

Dec 7

Chaos

8.5

 

Dec 9

Review Laplace transform problems, MINI-PROJECT #2 DUE

Dec 14 or 16

FINAL EXAM